A NUMERICAL STUDY OF THE SUDDEN ERUPTION OF SHEARED MAGNETIC-FIELDS

We investigate the quasi-static evolution of an idealized magnetic configuration in the solar corona that is subjected to photospheric shearing motions. The initial, unsheared field in our calculations is a magnetic dipole located at the center of the Sun. The assumed photospheric shearing motions are latitude-dependent and antisymmetric about the equator. The quasi-static evolution of the coronal field is calculated using the magneto-frictional method. A key difference between our study and previous work is that the outer computational boundary is placed exceedingly far from the solar surface where the shearing motions are applied. This is achieved by writing the basic equations of the magneto-frictional method in terms of the logarithm of radial distance. We find that initially, the coronal magnetic field expands steadily as the footpoint displacement is increased. However, when the footpoint displacement exceeds a certain critical amount, the qualitative behavior of the evolving field suddenly changes, so that the outward expansion of the field lines becomes a much more rapidly increasing function of the footpoint displacement. We propose that this sudden transition to a regime with very sensitive dependence on boundary conditions plays an important role in the onset of eruptive phenomena in the solar atmosphere.